Machine Learning-Enhanced Orbital-Free Density Functional Theory

Orbital-free density functional theory (OF-DFT) is the ultimate large-scale ab initio method, allowing calculations with 10⁶ atoms and beyond to be done relatively routinely with relatively modest computational resources. The key bottleneck to its wider adoption in applications is the accuracy of kinetic energy functionals (KEF). An important restriction is also the availability and accuracy of pseudopotentials (PP) that can be used with OF-DFT. Machine learning (ML) has recently emerged as a viable approach to construct KEFs and OF-DFT-suited PPs, expanding the domains of applicability of OF-DFT, as well as to predict electron density. We review works to date on ML-based construction of KEFs, PPs, and related works on ML of electron density and discuss the use of various ML methods (from neural networks to kernel regressions to symbolic regressions), the data aspect of the problem, connections to other applications, and perspectives of ML-based OF-DFT going forward.